U.S. patent number 6,690,023 [Application Number 09/930,064] was granted by the patent office on 2004-02-10 for methods and apparatus for providing a broadband tunable source of coherent millimeter, sub-millimeter and infrared radiation utilizing a non-relativistic electron beam.
Invention is credited to Anissim A. Silivra.
United States Patent |
6,690,023 |
Silivra |
February 10, 2004 |
Methods and apparatus for providing a broadband tunable source of
coherent millimeter, sub-millimeter and infrared radiation
utilizing a non-relativistic electron beam
Abstract
Techniques for super broadband operation of a long wavelength
free-electron laser (FEL) on a non-relativistic electron beam are
described. Because of the physical nature of the underlying
instability, a frequency region within which amplification or
generation of the electromagnetic waves occurs, ranges from
frequencies slightly below to many times above the resonant FEL
frequency. Therefore, in this regime, the device operating
frequency is determined by the frequency characteristics of a
device resonator and can be tuned over a wide range without
changing the electron beam energy or wiggler period. The upper
limit of the frequency band is imposed by the thermal spread in an
electron beam. Although this regime cannot be understood (and,
consequently, was not discovered) without using the relativistic
equation of motion, the regime does not rely upon relativism of an
electron beam. A non-relativistic implementation of this regime in
a submillimeter/THz device is advantageously described.
Inventors: |
Silivra; Anissim A. (Chapel
Hill, NC) |
Family
ID: |
26919759 |
Appl.
No.: |
09/930,064 |
Filed: |
August 15, 2001 |
Current U.S.
Class: |
250/492.3;
250/493.1 |
Current CPC
Class: |
H01S
3/0903 (20130101); H05G 2/00 (20130101); H05H
7/04 (20130101) |
Current International
Class: |
H05H
7/00 (20060101); H05H 7/04 (20060101); H05G
2/00 (20060101); A61N 005/00 () |
Field of
Search: |
;250/492.3,493.1
;372/2 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Pham; Hai
Assistant Examiner: Nguyen; Lam
Attorney, Agent or Firm: Priest & Goldstein, PLLC
Parent Case Text
RELATED APPLICATIONS
The present invention claims the benefit of U.S. Provisional
Application Serial No. 60/225,601 entitled "Methods and Apparatus
for Providing a Broadband Tunable Source of Coherent Millimeter
Sub-Millimeter and Infrared Radiation Utilizing a Non-Relativistic
Electron Beam" and filed Aug. 15, 2000.
Claims
I claim:
1. An electron device that includes an electron gun for producing a
non-relativistic electron beam; and means for creating a uniform
axial magnetic field B.sub.0 and a helical transverse magnetic
field of wiggler B.sub.w within a device interaction region wherein
the axial and transverse magnetic fields are such that said
electron beam moves along a helical trajectory with the transverse
velocity v.sub.195 and the longitudinal velocity v.sub.81
satisfying the following relation ##EQU25##
where v.sub.195, v.sub.81 are the transverse and longitudinal
electron velocity, .LAMBDA..sub.w is the spatial period of the
transverse magnetic field, ##EQU26##
is the spatial period of the cyclotron revolution of the electron
in the axial guide field, e and m are the charge and mass of the
electron respectively, c is the speed of light in vacuum.
2. A method of operating an electron device that includes an
electron gun for producing a non-relativistic electron beam
comprising the steps of: creating a uniform axial magnetic field
B.sub.0 ; and creating a helical transverse magnetic field B.sub.w
within a device interaction region wherein the axial and transverse
magnetic fields are such that said electron beam moves along a
helical trajectory with the transverse velocity v.sub.195 and the
longitudinal velocity v.sub.81 satisfying the following relation
##EQU27##
where .LAMBDA..sub.w is the spatial period of the transverse
magnetic field, ##EQU28##
is the spatial period of the cyclotron revolution of the electron
in the axial guide field, e and m are the charge and mass of the
electron respectively, c is the speed of light in vacuum.
Description
FIELD OF THE INVENTION
The present invention relates generally to improved methods and
apparatus for broadband tunable generation or amplification of
coherent electromagnetic radiation at millimeter, sub-millimeter
and infra-red wavelengths utilizing a non-relativistic electron
beam for terrestrial, space and air-born communication, radars,
semiconductor manufacturing, medical and other applications. More
particularly, an electron device consisting of an electron gun for
producing a non-relativistic electron beam, and techniques that are
described below for creating uniform axial magnetic field B.sub.0
and periodic transverse magnetic field B.sub.w within a device
interaction region so that said electron beam moves along a helical
trajectory with the transverse velocity v.sub..perp. and the
longitudinal velocity v.sub..parallel. satisfying the following
relationship ##EQU1##
where c is the speed of light in vacuum, .LAMBDA..sub.w is the
spatial period of the helical electron trajectory in the combined
field (it is also the spatial period of the transverse magnetic
field), .LAMBDA..sub.0 is the spatial period of the cyclotron
revolution of the electron in the axial guide field B.sub.0,
##EQU2##
v.sub..parallel. is the longitudinal electron velocity, e and m are
the charge and mass of the electron, respectively.
BACKGROUND OF THE INVENTION
Broadband tunable sources of electromagnetic radiation in
millimeter, submillimeter and far-infrared bands are widely sought
for a number of applications such as space and airborne
communication, radars, medical applications, semiconductor
manufacturing and others. Recently, broadband was added to a list
of requirements to be met for a number of broadband-hungry digital
wireless communication and Internet related applications. Although
this region of the electromagnetic spectrum cannot be labeled as
unreachable with traditional vacuum or quantum electronics devices,
the existing devices have low efficiency, narrow bandwidth and are
not tunable. The point is that this region of spectrum is situated
in between regions well occupied by vacuum electron devices such as
travelling wave tubes (TWT), backward wave oscillators (BWO),
klystrons and magnetrons on the mm wavelength side and solid state
quantum devices on the infrared and shorter wavelength side.
Traditional vacuum electron devices, such as traveling wave tubes
(TWTs), use either a slow-wave structure with the period
L.apprxeq.v.sub..parallel. /f, where f is the device operating
frequency, or in the case of the so-called gyro-devices, a high
intensity axial magnetic field B.sub.0 such that electron cyclotron
frequency ##EQU3##
is close to the device operating frequency. For the frequencies
above 300 GHz (wavelength of 1 mm or shorter), a slow-wave
structure with a period less than 1 mm would be required. In
addition to being not technologically feasible, in such small
period slow wave structures, it is impossible to realize efficient
interaction of an electromagnetic field with an electron beam. In
the case of gyro-devices at frequencies above 300 GHz, an axial
magnetic field stronger than 10 kGs would be required which cannot
currently be met in a portable device. Thus, further advance of the
traditional vacuum electronics into higher frequencies (shorter
wavelengths) requires development of new principles.
On the other hand, solid-state quantum devices are not efficient in
this region of the spectrum because the operating wavelength is too
long for quantum effects to be significant.
Among known devices, only free electron lasers (FEL) are efficient
in this region. The reason for this is probably the fact that the
FEL utilizes principles of quantum electronics in medium such as an
electron beam which is usual for classical vacuum electronics.
Thus, the essential parts of both quantum and classical electronics
are combined in this device. Unfortunately, for an FEL to operate
in the submillimeter region, an electron beam with the energy of at
least several MeVs is needed. Consequently, neither the dimensions
nor price of such an FEL are suitable for most of the applications
mentioned above.
SUMMARY OF THE INVENTION
The present invention further develops FEL principles leading to
the creation of novel tunable vacuum electron devices able to
generate and/or amplify electromagnetic radiation in the super-wide
wavelength band ranging from millimeters to far-infrared (or above
30 GHz to approximately 30 THz). The physical mechanism of such
devices is close to the mechanism of the wideband regime of long
wavelength FEL operation. Because of the physical nature of the
underlying instability, the FEL operating frequency in this regime
is not determined by the electron beam energy and wiggler field
period. It has been shown that a frequency region within which an
amplification or generation of electromagnetic waves occurs spans
from slightly below to far above the resonant FEL frequency.
Therefore, in practical implementations, the frequency band is
determined by the frequency characteristics of an FEL resonator and
interaction region. The frequency band can be widely tuned without
changing the electron beam energy and/or wiggler period. The
operating frequency band is upper limited by the thermal spread of
the electron beam. Although this regime cannot be understood
without using the relativistic equation of motion and,
consequently, was not discovered in the classical vacuum
electronics, the regime itself does not rely upon relativism of an
electron beam. Thus, a non-relativistic implementation of such
regime is possible.
To this end, an innovative approach for developing a source of
coherent electromagnetic radiation at frequencies 30 GHz and higher
is provided. Unlike traditional vacuum electron devices, the device
of the present invention does not utilize a strong axial magnetic
field or slow-wave structure, because it does not rely on beam-wave
synchronism. Instead, it uses a principle of parametric interaction
of waves in an electron beam which is successfully realized in
relativistic electronics, and in particular in free-electron lasers
(FELs).
A conventional FEL configuration is based on an interaction of a
fast electromagnetic mode of a waveguide (usually cylindrical) with
an electron beam which, under presence of combined axial guide
field and helical wiggler field, moves along a helical trajectory
with the spatial period equal to the period of the wiggler field,
.LAMBDA..sub.w. A beating between the electromagnetic wave and the
periodic transverse electron velocity produces a periodic
longitudinal force which affects the longitudinal motion of the
beam (this process is usually referred to as excitation of space
charge waves of an electron beam). Modulation of beam velocity
eventually results in modulation of beam density which, in its
turn, creates an up-frequency shifted electron current that
interacts with the initial electromagnetic wave. In other words, in
an FEL, a high-frequency electromagnetic wave interacts with the
space-charge waves of an electron beam and the interaction is
possible because electron motion is periodic in the presence of an
axial and a wiggler magnetic field as discussed further below.
Because of the fact that space charge waves have phase velocity
close to the longitudinal velocity of the electron beam,
v.sub..parallel., and the electromagnetic wave's phase velocity is
practically equal the speed of light, c, the interaction is
synchronous and leads to an amplification or generation of the
electromagnetic wave only within a narrow frequency band near the
resonant frequency ##EQU4##
Apparently, the resonant frequency could be very high for a
relativistic electron beam, when v.sub..parallel..fwdarw.c.
Unfortunately, a several MeV electron beam is required to produce
millimeter wave radiation, and the operating wavelength could only
be tuned at the expense of changing the electron beam energy or
wiggler field period both of which are not currently realizable in
any practical, portable application.
However, if a certain relation between the axial magnetic field and
transverse magnetic field holds, the FEL operational frequency band
greatly expands toward higher frequencies and, consequently, the
operating frequency is no longer determined by the resonance
formula above.
This regime features an interaction between different eigen modes
of the electron beam, namely cyclotron waves and space-charge
waves. Because the phase velocity of each of these waves does not
depend on the frequency (in fact, it is close to the longitudinal
beam velocity), a band of synchronism between waves becomes
extremely broad and ranges from slightly below to far above the
conventional FEL resonance frequency. The operating frequency band
is determined by the electrodynamic characteristics of the device
interaction region and device resonator. Thus, the electron device
can be tuned within the above said band without changing the
electron beam energy. The frequency band is up-limited by the
thermal velocity spread in the electron beam. For a good quality
electron beam, an estimated limiting frequency is on the order of
30 THz-100 THz.
Although this regime cannot be understood without using the
relativistic equation of motion of an electron beam, it does not
rely on the relativism of the longitudinal electron velocity. Among
its other aspects, the present invention advantageously realizes
this regime in a portable non-relativistic electron device.
These and other features, aspects and advantages of the invention
will be apparent to those skilled in the art from the following
detailed description taken together with the accompanying
drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 illustrates realizable steady-state trajectory of
non-relativistic electrons in a combined axial and wiggler
field;
FIG. 2 illustrates the dispersion relations for waves in the
system;
FIG. 3 shows a numerical solution of the non-reduced dispersion
relation for the non-relativistic case in accordance with the
present invention; and
FIG. 4 shows an exemplary broadband tunable electron device in
accordance with the present invention.
DETAILED DESCRIPTION
A free-electron laser (FEL) is presently the only vacuum electron
device that is tunable and can efficiently operate in the
submillimeter-far-infrared wavelength band. Such operation is
possible because FELs utilize a parametric synchronism of fast
electromagnetic modes of a smooth waveguide with an electron beam
(instead of a direct beam-wave synchronism that requires a
slow-wave structure with the period approximately equal to the
operating wavelength). Unfortunately, relativism of an electron
beam is a huge toll for shortening of the device operating
wavelength. An electron beam accelerated by at least several MeVs
is needed to produce sub-millimeter radiation with an FEL.
Obviously, the cost and dimensions of such a device do not suit any
portable application.
However, if a certain relation between FEL parameters (such as the
guiding magnetic field, the longitudinal beam velocity and the
period of the magnetic field) holds, the operating frequency band
of an FEL becomes extremely broad, and consequently, the operation
frequency is no longer determined by the conventional FEL relation.
A significant feature of this regime is that the frequency band
expands towards higher frequencies. As a result, a much higher than
conventional FEL frequency can be achieved without increasing the
electron beam energy. In fact, the energy of the electron beam can
be lowered to an unrelativistic level, which transforms the whole
device into a device of traditional vacuum electronics.
The first existence of unstable solutions in a broad frequency band
above the FEL resonance frequency was found under numerical
solution of the FEL dispersion relation in I.B. Bernstein, and L.
Friedland, Theory of the Free-Electron Laser with Combined Helical
Pump and Axial Guide Fields, Phys. Rev., vol. A-23 (1981) pp.
816-823. At about the same time, broadband radiation from an FEL
was registered experimentally as described in K.L. Felch, L.
Vallier et al, Collective Free-Electron Laser Studies, IEEE Journ.
Quantum Electronics, vol. QE-17(1981) pp. 1354-1356. In this
experiment a flat output radiation spectrum over a wavelength band
from 6 mm to 0.9 mm (from 50GHz to 350 GHz) was observed. The
results of this experiment were misinterpreted as a consequence of
a bad electron beam quality. Later a broadband regime of FEL
operation was studied theoretically from a standpoint of
interaction of eigen waves -of an electron beam. In the follow-up
experimental generator described in Yu.B. Victorov, A.B. Draganov
et al. Broadband Instability in Free-Electron Lasers, Optics
Communications, vol. 79, #1 (1990) pp. 81-87, ("Victorov") a
practically flat spectrum of the output radiation from 12 mm to 3.4
mm was observed with the electron efficiency of interaction of
about 10%. For the chosen magnitude of the wiggler field, the
broadband regime existed within a certain region of the guide field
magnitude close to the so-called cyclotron resonance. It should be
noted that generally accepted FEL theory predicted a resonant
regime of operation for the above mentioned device in the vicinity
of 8 mm (38 GHz) and was totally unable to explain an occurrence of
radiation with the wavelength shorter than 7 mm using realistic
assumptions of beam quality, etc. Different features related to
this FEL regime have been observed in several other independent
experiments.
Following Victorov, this regime features an interaction between
physically different eigen modes of an electron beam, namely
cyclotron waves and space charge waves. Because of the fact that
the phase velocity of the participating waves does not depend on
the frequency and essentially equals the longitudinal beam
velocity, the range of frequencies over which the synchronism
between waves holds, is extremely broad, anywhere from slightly
less than the conventional FEL resonance frequency to more than
10-100 times the resonance frequency. Thus, under this regime, the
device operation frequency is no longer equal to the FEL resonance
frequency, but is somewhere within the broad band of the wave
synchronism.
The present invention recognizes that since the nature of this
synchronism does not stem from the beam relativism, it can be
realized in a non-relativistic electron beam as well, thus allowing
a very high operating frequency to be achieved without using a
small period slow-wave structure or an extremely high magnitude of
magnetic field. In other words, borrowing the principle of
broadband synchronism under parametric interaction of
electromagnetic waves with an electron beam from the relativistic
electronics and implementing this principle in a device with a
non-relativistic electron beam can result in a breakthrough of the
vacuum electronics into the previously unreachable region of
sub-millimeter and far-infrared wavelengths.
To address underlying physical phenomena of the present invention,
let us consider a model of a transverse-uniform electron beam
moving in a combined uniform axial magnetic field B.sub.0 =B.sub.0
e.sub.z and periodic transverse magnetic (wiggler) field
##EQU5##
As is well known, in this field, electrons move along a
steady-state trajectory ##EQU6##
The constants of motion, or the steady-state transverse
v.sub..perp. and longitudinal velocity v.sub..parallel., are
determined as a solution to the following system of equations
##EQU7##
where .OMEGA..sub.0,w =eB.sub.0,w /(mc), e, m and .gamma. are the
electron charge, mass and relativistic factor respectively, and c
is the speed of light.
The system of equations (2) has four solutions in a general case.
Realizable solutions that satisfy a condition v.sub..parallel.
>0 are shown in graph 100 of FIG. 1. Further, we will only be
interested in region where
.vertline..DELTA..vertline.=.vertline..OMEGA..sub.0
/.gamma.-k.sub.w v.sub..parallel..vertline.<<.OMEGA..sub.0
/.gamma..
Since electrons move along the steady state trajectory, they form a
flow that can be described by the relativistic equation of motion
in Euler's form (a hydrodynamic approach) ##EQU8##
One can easily verify that the solution of equations (1) and (2)
satisfies the equation (3) when E=0 and ##EQU9##
The electromagnetic field E, B is described by Maxwell's equations,
which in this case have the form ##EQU10##
where the first equation is coupled with the equation of motion
through the electron current term j=-env, n is the density of the
electron beam.
To find the waves that can exist in this model, the linearization
procedure is used. Within this procedure all variables are
presented as a sum of a steady state value and as a small
perturbation:
then the system of equations is linearized with respect to the
perturbations.
The resulting system of equations has a simpler form when the
transverse components of the electromagnetic field and electron
velocity are expressed via partial amplitudes of right-hand
(A.sub.+ =A.sub.x +iA.sub.y) and left-hand (A.sub.- =A.sub.x
-iA.sub.y) circular polarized waves.
The equations for the transverse components have the form
##EQU11##
The equations for the longitudinal components have the form
##EQU12##
It is clearly seen that the system of equations (6) and (7) is
consistent if the solution for the transverse waves is proportional
to exp i[.omega.t-(k.-+.k.sub.w)z] and for the longitudinal waves
to exp i[.omega.t-kz]. Assuming that coupling coefficients are
small enough to be neglected, participating waves can be easily
identified.
The transverse waves are forward and backward electromagnetic waves
(of two different polarizations) passively coupled with the fast
(wave index +) or slow (wave index -) cyclotron modes of the
election beam. The corresponding dispersion relation has the form
##EQU13##
where .omega..sub.b =(4.pi.n.sub.0 e.sup.2 /m).sup.1/2 is the
plasma frequency of the election beam. Note, that because of the
transverse velocity modulation caused by the wiggler field, the
wave number of the transverse waves has a parametric shift
.-+.k.sub.w.
The longitudinal waves are space charge waves of the electron beam.
The dispersion relation for them has the form
In a non-relativistic case, that is central in the following
consideration, this dispersion relation reduces to the well known
(.omega.-kv.sub..parallel.).sup.2 =.omega..sub.b.sup.2. The
dispersion relations for all eight waves, collectively 200, are
sketched in FIG. 2 to make the following consideration clearer.
As is known from the general theory of waves and instabilities in
plasma, points of intersection of dispersion curves for different
types of waves are points in the vicinity of which a wave
instability may develop. In the system under consideration, an
instability may develop if one of participating waves is either the
slow space charge or the slow cyclotron wave. The intersection
point of space charge modes with the electromagnetic wave
corresponds to a conventional FEL resonance and has been
extensively analyzed elsewhere. The intersection point of the
cyclotron wave with the electromagnetic wave was analyzed in A. A.
Silivra, FEL on the Slow Cyclotron Wave, NIMPR, vol. A375, 1996,
pp.248-251. One more and absolutely unique possibility to realize
an instability in the system is to bring into synchronism the fast
and slow cyclotron waves of the electron beam.
Usually, the frequency offset between cyclotron waves, 2.DELTA., is
large enough to prevent synchronism of the cyclotron waves. In this
case, the coupling between cyclotron waves is negligibly small and
their dispersions may be analyzed separately similar to the case
shown in FIG. 2. But the situation is quite different in the
vicinity of the so-called cyclotron resonance of the transverse
velocity which takes place when the electron cyclotron frequency,
.OMEGA..sub.0 /.gamma., is close to the bounce frequency of
electrons in the wiggler field, k.sub.w v.sub..parallel.. Thus, the
denominator in the first formula (2) is small,
.DELTA.=.OMEGA..sub.0 /.gamma.-k.sub.w v.sub..parallel.
<<.OMEGA..sub.0 /.gamma., k.sub.w v.sub..parallel., and the
transverse velocity is relatively high, although a parameter
.beta..sub..perp..sup.2 =v.sub..perp..sup.2 /c.sup.b 2 is always
small .beta..sub..perp..sup.2 <<1. In FIG. 1, the cyclotron
resonance of the transverse electron velocity takes place where the
longitudinal electron velocity is represented by a steeper part of
the velocity curve.
The cyclotron resonance of the transverse steady state electron
velocity has a profound impact on the dispersion of the cyclotron
waves. Indeed, under these same circumstances, a relativistic
correction to the dispersion of cyclotron waves, k.sub.w
v.sub..parallel..gamma..beta..sub..perp..sup.2 /2, becomes
significant. Although the correction is relatively small, the
cyclotron wave offset .DELTA. is also small. That is why the small
relativistic correction may become large enough to significantly
reduce or even fully compensate the offset of the cyclotron waves
and bring them to synchronism.
To verify this statement, let us analyze the system described by
equations (6) and (7) at frequencies where the plasma frequency
influence on the dispersion is negligibly small, .omega..sub.b
/.omega.<<1. An asymptotic form of the dispersion relation
for the cyclotron branches of the transverse waves is the following
##EQU14##
where .DELTA..sub.mod =.DELTA.-k.sub.w
v.sub..parallel..gamma..beta..sub..perp..sup.2 /2. Thus, the
dispersion relations are straight lines shifted above and below the
line .omega.=kv.sub..parallel. by .DELTA..sub.mod. Because of the
relativistic correction, the shift .DELTA..sub.mod may become
smaller than the coupling coefficient between cyclotron waves. In
other words, if ##EQU15##
the fast and slow cyclotron waves of the electron beam are brought
into synchronism. As can be seen from FIG. 2, if the synchronism of
waves results in an instability, the instability should be
extremely broadband.
The simplest way to consider interaction of waves and find the
instability rate is the so-called method of weakly coupled waves.
Let us first neglect coupling between transverse and longitudinal
waves and find the following relations between wave components:
##EQU16##
where .chi..sub..+-..sup.2 =.omega..sup.2 -c.sup.2
(k.-+.k.sub.w).sup.2. After that, the equations for the transverse
waves take the following form ##EQU17##
Making the determinant of this system equal to 0 gives rise to the
dispersion equation for the waves under consideration.
Asymptotically, at frequencies much higher than the plasma
frequency of the electron beam, the dispersion relation takes the
form ##EQU18##
where the term in the night hand side represents the coupling
between waves. The dispersion of the waves is indeed represented by
straight lines in coordinates (.omega., k). If coupling between
waves is stronger than the waves' offset ##EQU19##
the waves become unstable with the instability rate ##EQU20##
that does not depend on the wave frequency.
Having introduced .delta.=.gamma.k.sub.w
v.sub..parallel..beta..sub..perp..sup.2 /2, the coupling
coefficient in equation (14) can be written in the form
.DELTA.(2.delta.-.DELTA.). Normalized dependence of the coupling
coefficient on the axial magnetic field as shown in FIG. 1 by
dashed line 102 has a distinct maximum in full consistence with the
experimental results of Victorov. Note, that instability may exist
only if .DELTA.(2.delta.-.DELTA.)>0.
A numerical solution of the non-reduced dispersion relation
obtained from equations (6) and (7) is given in FIG. 3. This
solution shows the dependence of the instability rate on the beam
plasma frequency which was not possible to determine in the
simplified consideration above.
In the non-relativistic limit (.gamma..fwdarw.1) the criterion for
this instability reduces to ##EQU21##
which after simple transformation can be written as follows
##EQU22##
where ##EQU23##
is the spatial period of the cyclotron revolution of the electron.
Note that both the longitudinal v.sub..parallel. and transverse
v.sub..perp. electron velocity depend on magnetic fields B.sub.0,w
in accordance with equations (1) and (2).
It is important to note that the instability extends towards
infinitely high frequencies only within the frame of the
hydrodynamic consideration developed above. A thermal velocity
spread V.sub.T in the electron beam limits the frequency of the
instability at ##EQU24##
For high quality non-relativistic electron beams, the limiting
wavelength can be as short as 10 .mu.m.
As an example of a nonrelativistic implementation, let us consider
a device with the following parameters: beam voltage U=10 kV, beam
current I=100 mA, axial magnetic field B.sub.0 =1 kGs, wiggler
magnetic field B.sub.w =30 Gs, wiggler period .LAMBDA..sub.w =1 cm
(k.sub.w =6.28 cm.sup.-1). Under these parameters, the normalized
transverse velocity .beta..sub..perp. =0.17 and longitudinal
velocity .beta..sub..parallel. 0.09, while the radius of the
corresponding steady-state trajectory R=3 mm. For .omega..sub.b
=10.sup.9 s.sup.-1, the instability rate is -Im.omega.=10.sup.-3
k.sub.w c.apprxeq.2.2.multidot.10.sup.8 s.sup.-1 and is suitable
for implementation in generators and amplifiers.
FIG. 4 shows an exemplary broadband tunable electron device 400 in
accordance with the present invention. Device 400 comprises an
electron gun, a wiggler field system 404, an axial magnetic field
system 406, and a control system 408 which cooperate to control an
electron beam 410 to produce output radiation 412, as discussed in
detail above. Control system 408 may be suitably implemented
utilizing a control processor programmed to provide control outputs
to the electron gun 402, wiggler field system 404 and axial field
magnetic field system 406 so that device 400 operates in the
desired region.
While the present invention has been disclosed in the context of
various aspects of a presently preferred embodiment, it will be
recognized that many variations may be made to adapt the present
teachings to other contexts consistent with the claims that follow.
Simply by way of example, it is anticipated that an FEL in
accordance with the present invention may find application for
terrestrial, space and air-born communication, radar, medical
applications, semiconductor manufacturing and other areas which
will be apparent to those of skill in the art.
* * * * *